Grid Spacing Selection

The choice of timestep and grid size for an explicit time advancement is a relative matter and is theoretically based on the well-known Courant condition (Basco, 1978). The choice of grid size usually depends on available topographic data for nodal elevation determination and the size of the problem. The effect of the grid size (for constant timestep for 7.2 seconds) on the diffusion model accuracy can be shown by example where nodal spacings of 1,000, 2,000 and 5,000-feet are considered. The predicted flood depths varied only slightly from choosing the grid size between 1,000-feet and 2,000-feet. However, an increased variation in results occurs when a grid size in 5,000-feet is selected. For the example of peak flow rate test hydrograph of 600,000 cfs, the differences of simulated flow depths between 1,000-feet and 5,000-feet grid are 0.03 feet, 0.06 feet and 0.17 feet at 1 mile, 5 miles and 10 miles, respectively, downstream from the dam-break site for the maximum flow depth with the magnitude of 30 feet.

Because the algorithm presented is based upon an explicit timestepping technique, the modeling results may become inaccurate should the timestep size versus grid size ratio become large. A simple procedure to eliminate this instability is to half the timestep size until convergence in computed results is achieved. Generally, such a timestep adjustment may be directly included in the computer program for the dam-break model. For the cases considered in this section, timestep size of 7.2 second was found to be adequate when using the 1,000-feet to 5,000-feet grid sizes.

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